A Hybrid Truncated Norm Regularization Method for Matrix Completion.

Area of Science:

• Computer Science
• Applied Mathematics

Background:

• Matrix completion is crucial in image processing, often treated as a low-rank matrix approximation problem.
• Existing methods face challenges with stability and computational cost in complex models.

Purpose of the Study:

• To propose a novel regularization method for matrix completion.
• To enhance the stability and recovery performance of matrix completion models.

Main Methods:

• Introduced truncated Frobenius norm (TFN) and a hybrid truncated norm (HTN) model.
• Developed a two-step iteration algorithm with adaptive penalty parameter adjustment.
• Provided mathematical proof for the convergence of the proposed method.

Main Results:

• The hybrid truncated norm (HTN) model significantly improves recovery performance and model stability.
• The adaptive penalty parameter reduces computational costs.
• The method demonstrates competitive success in synthetic data, real-world images, and recommendation systems.

Conclusions:

• The proposed hybrid truncated norm (HTN) method offers a stable and effective solution for matrix completion.
• This approach outperforms existing state-of-the-art methods in various applications.
• The method effectively mitigates large variations in complex model estimations.